Known shaft preheaters for preheating material in lump form ahead of downstream kilns frequently consist of a chamber which is formed as an annular shaft and in which the stock which is to be preheated is distributed. The stock is as a rule delivered into the preheater from a silo chamber lying above. The width of the annular shaft is limited to approximately 1.30 m in order to prevent segregation phenomena of the individual grain-size fractions. The preheated stock is discharged from the preheater via a plurality of rams disposed at the circumference. The flue gases from the downstream kilns are generally used for the preheating process by being delivered to the fill via horizontal bridges disposed in the annular shaft. However it has in this case been found that the material is heated relatively unevenly over the depth of the shaft, in particular when the shafts are relatively deep, due to the varying length of the fill through which the flue gases flow.